September Morn Update

Task/Vogels-approximation-method/Phix/vogels-approximation-method-1.phix

@@ -0,0 +1,68 @@
+sequence supply = {50,60,50,50},
+         demand = {30,20,70,30,60},
+         costs = {{16,16,13,22,17},
+                  {14,14,13,19,15},
+                  {19,19,20,23,50},
+                  {50,12,50,15,11}}
+
+sequence row_done = repeat(false,length(supply)),
+         col_done = repeat(false,length(demand))
+
+function diff(integer j, leng, bool is_row)
+integer min1 = #3FFFFFFF, min2 = min1, min_p = -1
+    for i=1 to leng do
+        if not iff(is_row?col_done:row_done)[i] then
+            integer c = iff(is_row?costs[j,i]:costs[i,j])
+            if c<min1 then
+                min2 = min1
+                min1 = c
+                min_p = i
+            elsif c<min2 then
+                min2 = c
+            end if
+        end if
+    end for
+    return {min2-min1,min1,min_p,j}
+end function
+
+function max_penalty(integer len1, len2, bool is_row)
+integer pc = -1, pm = -1, mc = -1, md = -#3FFFFFFF
+    for i=1 to len1 do
+        if not iff(is_row?row_done:col_done)[i] then
+            sequence res2 = diff(i, len2, is_row)
+            if res2[1]>md then
+                {md,mc,pc,pm} = res2
+            end if
+        end if
+    end for
+    return {md,mc}&iff(is_row?{pm,pc}:{pc,pm})
+end function
+
+integer supply_left = sum(supply),
+        total_cost = 0
+
+sequence results = repeat(repeat(0,length(demand)),length(supply))
+
+while supply_left>0 do
+    sequence cell = min(max_penalty(length(supply), length(demand), true),
+                        max_penalty(length(demand), length(supply), false))
+    integer {{},{},r,c} = cell,
+            q = min(demand[c], supply[r])
+    demand[c] -= q
+    col_done[c] = (demand[c]==0)
+    supply[r] -= q
+    row_done[r] = (supply[r]==0)
+    results[r, c] = q
+    supply_left -= q
+    total_cost += q * costs[r, c]
+end while
+
+printf(1,"     A   B   C   D   E\n")
+for i=1 to length(supply) do
+    printf(1,"%c ",'Z'-length(supply)+i)
+    for j=1 to length(demand) do
+        printf(1,"%4d",results[i,j])
+    end for
+    printf(1,"\n")
+end for
+printf(1,"\nTotal cost = %d\n", total_cost)

Task/Vogels-approximation-method/Phix/vogels-approximation-method-2.phix

@@ -0,0 +1,7 @@
+sequence supply = {461, 277, 356, 488,   393},
+         demand = {278, 60, 461, 116, 1060},
+         costs  = {{46, 74,  9, 28, 99},
+                   {12, 75,  6, 36, 48},
+                   {35, 199, 4,  5, 71},
+                   {61, 81, 44, 88,  9},
+                   {85, 60, 14, 25, 79}}